In 1982 Richard Feynman introduced the concept of a “quantum simulator.” See Feynman, 1982, “Simulating Physics with Computers”, Int. J. Theor. Phys. 21, p. 467, which is hereby incorporated by reference in its entirety. Soon thereafter it was determined that a quantum system could be used to yield a potentially exponential time saving in certain types of intensive computations. See Deutsch, 1985, “Quantum Theory, the Church-Tuning Principle and the Universal Quantum Computer”, Proc. of the Roy. Soc. of London A400, p. 97, which is hereby incorporated by reference in its entirety. Since then, further quantum computing research has provided significant software and hardware advances. As the speed of classical computers approaches a projected upper bound due to the natural limits of miniaturization of integrated circuits, the interest in quantum computers has intensified. Indeed many algorithms suitable for quantum computing have been written. Two notable examples of such algorithms are the Shor and Grover algorithms. See Shor, 1997, SIAM J. of Comput. 26, p. 1484; U.S. Pat. No. 6,317,766; and Grover, 1996, Proc. 28th STOC p. 212, which are hereby incorporated by reference in their entireties. Nevertheless, sizeable obstacles prevent the development of large-scale quantum computing devices that are practical and that are capable of out-performing known classical computers. See, for example, “Quantum Dreams”, The Economist, Mar. 10, 2001, pp. 81-82, which is hereby incorporated by reference in its entirety.
In fact, the field of quantum computing remained theoretical until the late 1990's when several hardware proposals were tested. Of these hardware proposals, the most scalable physical systems appear to be those that are superconducting structures. Superconducting material is material that has zero electrical resistance below critical levels of current, magnetic field and temperature. Josephson junctions are examples of such structures. In fact, Josephson junctions are of special interest because their observable properties are macroscopic manifestations of underlying quantum mechanical principles.
One physical realization of a quantum computer is based on quantum bits, or “qubits.” Generally speaking, a qubit is a well-defined physical structure that (i) has a plurality of quantum states, (ii) can be isolated from its environment and (iii) quantum tunneling between each of the quantum states can occur. See for example, Mooji et al., 1999, Science 285, p. 1036. A survey of the current physical systems from which qubits can be formed is found in Braunstein and Lo (eds.), 2001, Scalable Quantum Computers, Wiley-VCH Verlag GmbH, Berlin, which is hereby incorporated by reference in its entirety.
In order for a physical system to behave as a qubit a number of requirements must be satisfied. See DiVincenzo in Scalable Quantum Computers, chapter 1, Wiley-VCH Verlag GmbH, Berlin which is hereby incorporated by reference in its entirety. These requirements include the need for the physical system (qubit) to be scalable. In other words, it must be possible to combine a reasonable number of the qubits in a coherent fashion. Associated with scalability is the need to eliminate qubit decoherence. Also required for a qubit to be useful in quantum computing, is the ability to perform operations that initialize, control and couple the qubit. Control of a qubit includes performing single qubit operations as well as operations on two or more qubits. In order to support universal quantum computing, this set of operations needs to be a universal set. A universal set of quantum operations is any set of quantum operations that permits all possible quantum computations. Many sets of gates are universal, see Barenco et al., 1995, Physical Review A 52, p. 3457, which is hereby incorporated by reference in its entirety. Yet another requirement is the need to be able to measure the state of the qubit in order to perform computing operations and retrieve information.
There are two principal means to realize superconducting qubits. One means corresponds to the limits of well-defined charge (charge qubit). The other means corresponds to the limits of well-defined phase (phase qubit). Phase and charge are related variables that, according to basic quantum principles, are canonical conjugates of one another. The division of the two classes of devices is outlined in Makhlin et al., 2001, Reviews of Modern Physics 73, p. 357, which is hereby incorporated by reference in its entirety.
Materials that exhibit superconducting properties are attractive candidates for quantum computing applications, since the quantum behavior of the Bose condensates (Cooper pairs) at Josephson junctions have macroscopically observable consequences. Indeed, recently, several designs of a superconducting qubit have been proposed and tested. See, for example, Nakamura et al., 1999, Nature 398, p. 786; Friedman et al., 2000, Nature 406, p. 43; and van der Wal et al., 2000, Science 290, p. 773, which are hereby incorporated by reference in their entireties. The qubits described in these reference demonstrate the existence of qubits having potential energy states. The qubits described in these reference are not coupled and they are not controlled in a scalable manner. Therefore, the qubits described in these references do not satisfy all the requirements for universal quantum computing put forth by DiVincenzo.
The preferred type of superconducting material used to make a qubit depends on the nature of the qubit. Generally speaking, these materials are often divided into metal and oxides. However, the ability to deposit metals and oxides (that are not oxides of the deposited metal) on the same chip is expensive and time consuming. This is a concern because this form of deposition is needed in many types of qubit. Thus, known fabrication methods for forming many types of qubits is time consuming, expensive and difficult.
The quantum mechanical properties of a qubit are easily affected by interactions between the qubit and the environment (e.g., other systems). Yet quantum computing requires that the qubit be isolated from such interactions so that the state of the qubit can coherently evolve in accordance with a quantum gate that is applied to the qubit. Despite the requirement for isolation so that the qubit can evolve, universal quantum computing still requires some control over (interaction with) the qubit so that fundamental operations such as qubit initialization, gate application, and qubit state measurement can be effected. This apparent contradiction between the need for isolation and the need for control over the quibt is a direct result of the quantum behavior of qubits.
The need for isolated qubits that nevertheless can be controlled has presented numerous fabrication and design challenges. Such challenges have included identification of methods for initialization, control, coupling and measurement of qubits. Systems and methods for addressing these challenges are being investigated. In particular, systems in which qubits can be controlled and measured in ways that do not perturb their internal quantum states are being sought. Devices that include multiple controllable qubits that permit classical logic operations to be performed are central to the goal of building a quantum computer. To date, many known systems and methods for coupling model qubits in simulated quantum computing devices have been unwieldy and generally unsatisfactory. Such systems and methods are based on optics (entanglement of photons) or nuclear magnetic resonance (utilizing spin states of atoms and molecules).
Recently, however, inductive coupling between phase qubits has been described. See, for example, Orlando et al., 1999, “Superconducting Persistent Current Qubit”, Phys. Rev. B 60, p. 15398, and Makhlin et al., 2001, “Quantum-State Engineering with Josephson-Junction Devices”, Reviews of Modern Physics 73, p.357 (and in particular, page 369), each of which is incorporated herein by reference in their entireties. However, the qubits described in Orlando et al. have not been coupled and controlled in a scalable manner.
As discussed above, in order to effect quantum computing, a physical system containing a collection of qubits is needed. A qubit as defined herein is a quantum two-level system that is like the ground and excited states of an atom. The generic notation of a qubit state denotes one state as |0> and the other as |1>. The essential feature that distinguishes a qubit from a bit is that, according to the laws of quantum mechanics, the permitted states of a single qubit fills up a two-dimensional complex vector space; the general notation is written a|0>+b|1>, where a and b are complex numbers. The general state of two qubits, a |00>+b|01>+c|10>+d|11> is a four-dimensional state vector, one dimension for each distinguishable state of the two qubits. When an entanglement operation has been performed between the two qubits, their states are entangled. This means that they cannot be written as a product of the states of two individual qubits. The general state of n entangled qubits is therefore specified by a 2n-dimensional complex state vector. The creation of 2n-dimensional complex vectors provides one of the bases for the enormous computing potential of quantum computers. For more information on qubits and entanglement, see Braunstein and Lo (eds), 2001, Scalable Quantum Computers, Wiley-VCH, New York, which is incorporated herein by reference in its entirety.
Current methods for entangling qubits in order to realize 2n-dimensional complex state vectors are susceptible to loss of coherence. Loss of coherence is the loss of the phases of quantum superpositions in a qubit as a result of interactions with the environment. Loss of coherence results in the loss of the superposition of states in a qubit. See, for example, Zurek, 1991, Phys. Today 44, p. 36; Leggett et al., 1987, Rev. Mod. Phys. 59, p. 1; Weiss, 1999, Quantitative Dissipative Systems, 2nd ed., World Scientific, Singapore; and Hu et al; arXiv:cond-mat/0108339, which are hereby incorporated by reference in their entireties.
It has been proposed in the art that a superconducting resonator can be entangled with a qubit when the resonant frequency of the superconducting resonator is correlated with the energy difference between the basis states of the qubit. See, e.g., Buisson and Hekking, Aug. 18, 2000, “Entangled states in a Josephson charge qubit coupled to a superconducting resonator,” LANL cond-mat/0008275 and the references therein, and Al-Saidi and Stroud, Dec. 4, 2001 “Eigenstates of a small Josephson junction coupled to a resonant cavity”, Phys. Rev. B, 65, 014512 and the references therein, which are hereby incorporated by reference in their entireties. The entanglement proposed in these references causes the state of the charge qubit to be entangled with the state of the superconducting resonator, thus illustrating the potential for achieving entangled quantum states in a solid state design. However, the references do not provide methods for coherently entangling the quantum states of qubits in a solid-state design, nor do they demonstrate how such entanglement is useful for quantum computing.
The Josephson junction qubit has been proposed in the art. See, e.g. Martinis et al, “Rabi oscillations in a large Josephson junction qubit”, preprint presented at the American Physical Society (APS) 2002 Annual Meeting, held Jul. 27-31, 2002, and Han et al., 2001, Science, 293, 1457, which are hereby incorporated by reference in their entireties. In order to perform quantum computation, the basis states |0> and |1> of the Josephson junction qubit are allowed to evolve according to the rules of quantum mechanics. This quantum evolution is extremely sensitive to decoherence arising from various sources, such as thermal excitations or stray fields. Therefore, qubits must remain coherent in order to achieve scalable quantum computation. Previously, mechanisms proposed for controlling quantum evolution required microwave frequency current biasing of the already current biased Josephson junction qubit.
A problem that is therefore present in the art is the question of how to entangle qubits in order to realize a quantum register that can support quantum computing. In the art, some types of qubits are set to an initial state using means such as a dc current. Next, the qubits are permitted to tunnel between a base and first energy level quantum state. The tunneling, also termed evolution, is a necessary aspect of quantum computing. One means for allowing qubits to evolve is to apply an AC current. The problem, however, is that qubits that are permitted to tunnel between a base and first energy level quantum state using an AC current cannot easily be entangled with other qubits in order to achieve a 2n-dimensional complex state vector, where n is the number of qubits in the quantum register. Such entanglement is necessary in order to realize a quantum register that can support quantum computing. Given the above background, it is apparent that improved methods for permitting qubits to tunnel between a base and first energy level quantum state are needed in the art.
Like reference numerals refer to corresponding parts throughout the several views of the drawings.